Kode #105: hints & solution
Here's the clue board for Kode #105. Start with the spoiler-free hints. If you're still stuck, the full step-by-step solution is below, hidden until you open it.
The clue board
Each row is a guess that's already been graded. ▲ means a right digit in the right spot; ● means a right digit in the wrong spot.
- 10367▲1●1
- 28391▲0●2
- 31835▲1●1
- 49132▲0●2
- 50217▲0●0
Spoiler-free hints
- Exactly one of the four digits is even.
- The four digits add up to 23.
- 3 of the digits are 5 or higher.
Try the hints first. The solution below walks through every deduction.
Step-by-step solution
Every Kode can be cracked by pure deduction, with no guessing. This board falls in 10 logical steps. Open the solution to follow them one at a time.
Show the solution · reveals the code
When a row "rules out" a position, it shows that digit there but its ▲ marks are already used up (or it has none), so the digit can't sit there.
- Row 5 (0 2 1 7) has no marks at all, so 0, 2, 1, and 7 are not in the code.
- Row 1 (0 3 6 7) has 2 marks still unexplained, and only 2 digits are left undecided: 3 and 6. So both are in the code.
- Row 4 (9 1 3 2) has one mark still unexplained, and only one digit is left undecided: 9. So it is in the code.
- Row 2 (8 3 9 1) has 2 marks, already accounted for by 3 and 9. That rules out 8.
- Row 3 (1 8 3 5) has one mark still unexplained, and only one digit is left undecided: 5. So it is in the code.
- That makes all four digits of the code: 3, 5, 6, and 9. Every other digit is out, which also rules out 4.
- Row 1 (0 3 6 7) has one digit in the right spot. Since row 2 rules out the 3 in position 2, it has to be the 6 in position 3.
- Row 3 (1 8 3 5) has one digit in the right spot. Since position 3 is already 6, it has to be the 5 in position 4.
- The 3 has only one spot left: position 1 (row 2 rules out position 2, position 3 is already 6, and position 4 is already 5).
- That leaves the 9 for position 2.
That cracks it: the code is 3965.